Liberal Democrats gave their clearest public signal of disquiet over their party's role in the coalition today as they voted to campaign against the flagship Tory policy of free schools.

The party's conference in Liverpool overwhelmingly backed a motion that attacks free schools because they risk "increasing social divisiveness and inequity in a system that is already unfair".

The vote means the Lib Dems are committed to lobbying against a key plank of government education policy. Michael Gove, the Tory education secretary, believes that a new generation of "independent state schools" with small classes and firm discipline will reduce inequality in England's education system.

Peter Downes, a retired headteacher and Lib Dem councillor who tabled the motion, said the most disturbing aspect of the coalition policy was "the idea that the principles of the market place can be applied to state-funded education".

"Free schools will provide competition so that underperforming or failing schools will have to improve their performance or wither and die," he said. "Just as the supermarket drives the corner shop out of business, so it will be with schools.

"When Sainsbury's provides some new products to lure people away from their competitors, the unsold items in the failing shops can be returned to the wholesaler or sold off in a sale. But not so in schools. Pupils are human beings, not tins of beans." The motion also expresses concern about the coalition government's expansion of academies and says councils must retain oversight of school places funded by the taxpayer.

The party's leadership sought to contain the revolt with an amendment that softened the wording, from calling on Liberal Democrats to campaign against free schools to urging the party's peers and MPs to work within Westminster to strengthen the role of local authorities and ensure the creation of new free schools does not harm existing state schools. This amendment was rejected by delegates.

Earlier this month Gove announced the first 16 free school proposals to have won initial approval. The schools are due to open next September and include one in west London which will have compulsory Latin lessons, and another in Bedford where every child will be encouraged to play an instrument. Critics fear the new schools will increase social segregation – a concern fuelled by the fact that seven of the first 16 have religious affiliations.

The government has also accelerated the expansion of academies, pushing through a law shortly after the coalition was formed that enabled every school in England to convert to give them independence of local authorities and power to set their own pay and opt out of the national curriculum. Sarah Teather, a Lib Dem education minister, said she was "secretly rather proud and relieved" to find the party's conference making trouble even when the Lib Dems were in government. But she urged delegates to vote against the motion, saying the party could have more impact in government than in opposition.

A majority of delegates who spoke in the debate joined in the attack on coalition policy. Kath Pinnock, a Lib Dem councillor in Yorkshire, described a local free school proposal that she said "threatens the viability of a very good secondary school".

She said she was concerned that the school could set its catchment area, which she claimed would lead to the exclusion of children from deprived neighbourhoods. The vote was welcomed by teaching unions and opens up the prospect of Lib Dems teaming up with union activists to fight against free school proposals. Meanwhile Nick Clegg sought to reassure Liberal Democrat activists in his setpiece speech this afternoon, praising the party's "passion for education" and contrasting the coalition's plans with Labour's academies programme, which focused on struggling schools in the poorest areas.

Clegg described this as "a few schools singled out for preferential treatment – a cuckoo in the nest that eats up attention and resources". "We're opening up the option of academy freedom to all schools … my vision is that every school, in time, will be equal, every school equally free."

A coalition source said the vote was a part of "healthy debate" within the Liberal Democrats. The government source said: "Our legislation was improved by Liberal Democrat input and there is no doubt that constructive and open debate will further improve our policies."

Ed Balls, the shadow education secretary, said the vote was "another blow for the coalition's unpopular, flawed and deeply unfair school reforms".